Spurs, who host Manchester City in their Premier League opener on Saturday followed by a Champions League playoff first-leg tie at Young Boys of Berne on Tuesday, need more depth in central defence to compete on four fronts this season.
"I like Gallas. I think he's a great free transfer. I thought at the start of the year there were three fantastic free transfers available - (goalkeeper) David James, Joe Cole and William Gallas," Redknapp told reporters.
"It's a possibility to (sign Gallas). His wages aren't a problem. He has not been greedy at all. His people have rung up and we spoke about it," he added, rating his chances of acquiring the 32-year-old former Arsenal captain at 50-50.
Asked whether the Spurs fans would object to the signing of an Arsenal stalwart, Redknapp said: "You can go on forever about that. He played for Chelsea as well.
"We put too much importance on that all the time. If he comes in and plays rubbish then the crowd will slaughter him. If he comes in and plays great they will love him."
The long-term injured Jonathan Woodgate is unlikely to make the club's 25-man Premier League squad this season and Ledley King suffers with persistent knee problems that means he will not be risked in Tuesday's tie on synthetic turf in Switzerland.
"It is about time somebody else won the championship. It is not impossible and that is what I will tell the players tomorrow," said the Spurs manager after watching the players put through their paces in a training match.
"If I get who I want they would be fantastic for us. We could be close (to the title) if we get them," he added.
"We've got to push on if we want to - now's (our) chance. We were behind Arsenal by miles for years and years but now we've got a chance to really push them and get above them.
"That would be great for Tottenham fans and it's possible. We could be close to the title. We just need to improve that little bit now and if we could do that it could happen."
